Subgroups — C₃₁×#34974 #21491733

Order 7936.

1918 conjugacy classes of subgroups.

The subgroup lattice has 976 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#2532	C₂	1	2	yes	maximal, complemented
2	C₃₁×#2529	C₂	1	2	yes	maximal, complemented
3	C₃₁×#2512	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#2508	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#2495	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#2491	C₂	1	1	yes	maximal, characteristic
7	C₃₁×#2479	C₂	1	2	yes	maximal, complemented
8	C₃₁×#2474	C₂	1	2	yes	maximal, complemented
9	C₃₁×#2451	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#2448	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#2426	C₂	1	1	yes	maximal, characteristic
12	C₃₁×#2423	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#2396	C₂	1	2	yes	maximal, complemented
14	C₃₁×#2395	C₂	1	2	yes	maximal, complemented
15	C₄×C₃₁×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₃₁×#126	C₂	1	2	yes	maximal, complemented
17	C₄×C₃₁×#124	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×C₃₁×#124	C₂	1	2	yes	maximal, complemented
19	C₄×C₃₁×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×C₃₁×#121	C₂	1	1	yes	maximal, characteristic
21	C₃₁×#2293	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄²×Q₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×C₃₁×#117	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₃₁×#126	C₂²	1	2	yes	—
26	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
27	C₂×C₃₁×#124	C₂²	1	2	yes	—
28	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
33	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
36	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
37	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
38	C₂×C₃₁×#117	C₂²	1	2	yes	—
39	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
40	C₃₁×#400	C₂²	1	2	yes	—
41	C₃₁×#400	C₂²	1	2	yes	—
42	C₃₁×#399	C₂²	1	2	yes	—
43	C₃₁×#399	C₂²	1	2	yes	—
44	C₃₁×#398	C₂²	1	2	yes	—
45	C₃₁×#398	C₂²	1	2	yes	—
46	C₃₁×#398	C₂²	1	2	yes	—
47	C₃₁×#397	C₂²	1	2	yes	—
48	C₃₁×#397	C₂²	1	2	yes	—
49	C₃₁×#397	C₂²	1	2	yes	—
50	C₃₁×#396	C₂²	1	2	yes	—
51	C₃₁×#396	C₂²	1	2	yes	—
52	C₃₁×#395	C₂²	1	2	yes	—
53	C₃₁×#394	C₂²	1	2	yes	—
54	C₃₁×#394	C₂²	1	2	yes	—
55	C₃₁×#393	C₂²	1	2	yes	—
56	C₃₁×#391	C₂²	1	2	yes	—
57	C₃₁×#391	C₂²	1	1	yes	characteristic
58	C₃₁×#391	C₂²	1	1	yes	characteristic
59	C₃₁×#391	C₂²	1	2	yes	—
60	C₃₁×#390	C₂²	1	2	yes	—
61	C₃₁×#390	C₂²	1	1	yes	characteristic
62	C₃₁×#390	C₂²	1	1	yes	characteristic
63	C₃₁×#390	C₂²	1	1	yes	characteristic
64	C₃₁×#390	C₂²	1	1	yes	characteristic
65	C₃₁×#389	C₂²	1	1	yes	characteristic
66	C₃₁×#389	C₂²	1	1	yes	characteristic
67	C₃₁×#389	C₂²	1	2	yes	—
68	C₃₁×#389	C₂²	1	1	yes	characteristic
69	C₃₁×#389	C₂²	1	1	yes	characteristic
70	C₃₁×#389	C₂²	1	1	yes	characteristic
71	C₃₁×#389	C₂²	1	1	yes	characteristic
72	C₃₁×#388	C₂²	1	2	yes	—
73	C₃₁×#388	C₂²	1	2	yes	—
74	C₃₁×#388	C₂²	1	2	yes	—
75	C₃₁×#388	C₂²	1	2	yes	—
76	C₃₁×#388	C₂²	1	2	yes	—
77	C₃₁×#388	C₂²	1	2	yes	—
78	C₃₁×#388	C₂²	1	2	yes	—
79	C₃₁×#388	C₂²	1	2	yes	—
80	C₃₁×#388	C₂²	1	2	yes	—
81	C₃₁×#388	C₂²	1	2	yes	—
82	C₃₁×#388	C₂²	1	2	yes	—
83	C₃₁×#388	C₂²	1	2	yes	—
84	C₃₁×#387	C₂²	1	2	yes	—
85	C₃₁×#387	C₂²	1	2	yes	—
86	C₃₁×#387	C₂²	1	2	yes	—
87	C₃₁×#387	C₂²	1	2	yes	—
88	C₃₁×#386	C₂²	1	2	yes	—
89	C₃₁×#385	C₂²	1	2	yes	—
90	C₃₁×#384	C₂²	1	1	yes	characteristic
91	C₃₁×#383	C₂²	1	2	yes	—
92	C₃₁×#382	C₂²	1	1	yes	characteristic
93	C₃₁×#382	C₂²	1	2	yes	—
94	C₃₁×#380	C₂²	1	1	yes	characteristic
95	C₃₁×#380	C₂²	1	1	yes	characteristic
96	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
97	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
98	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
99	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
100	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
101	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
102	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
103	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
104	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
105	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
106	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
107	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
108	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
109	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
110	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
111	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
112	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
113	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
114	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
115	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
116	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
117	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
118	C₃₁×#376	C₂²	1	1	yes	characteristic
119	C₃₁×#376	C₂²	1	1	yes	characteristic
120	C₄³×C₃₁	C₂²	1	1	yes	characteristic
121	C₄³×C₃₁	C₂²	1	1	yes	characteristic
122	C₄³×C₃₁	C₂²	1	2	yes	—
123	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
124	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
125	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
126	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
127	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
131	C₃₁×C₄⋊Q₈	—	2	4	no	—
132	C₃₁×#126	—	2	8	no	—
133	C₃₁×#124	—	2	4	no	—
134	C₃₁×#124	—	2	8	no	—
135	C₃₁×C₂²⋊Q₈	—	2	4	no	—
136	C₃₁×#121	—	2	4	no	—
137	C₄×Q₈×C₃₁	—	2	4	no	—
138	C₄×Q₈×C₃₁	—	2	4	no	—
139	C₄×Q₈×C₃₁	—	2	4	no	—
140	C₄×Q₈×C₃₁	—	4	4	no	—
141	C₄×D₄×C₃₁	—	2	4	no	—
142	C₄×D₄×C₃₁	—	4	4	no	—
143	C₃₁×#117	—	2	4	no	—
144	C₃₁×#117	—	2	4	no	—
145	C₃₁×#117	—	4	4	no	—
146	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
151	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
152	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
153	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
157	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
158	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
159	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
160	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
161	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
168	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
169	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
174	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
175	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
178	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
180	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
181	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
183	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
185	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
186	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
187	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
188	C₂×C₄²×C₃₁	—	2	4	no	—
189	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
198	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
199	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
201	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
202	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
203	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
204	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
206	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
207	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
208	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
209	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
210	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
211	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
212	C₃₁×#95	C₂³	1	2	yes	—
213	C₃₁×#95	C₂³	1	2	yes	—
214	C₃₁×#95	C₂³	1	2	yes	—
215	C₃₁×#95	C₂³	1	1	yes	characteristic
216	C₃₁×#95	C₂³	1	2	yes	—
217	C₃₁×#95	C₂³	1	1	yes	characteristic
218	C₃₁×#95	C₂³	1	1	yes	characteristic
219	C₃₁×#95	C₂³	1	2	yes	—
220	C₃₁×#95	C₂³	1	2	yes	—
221	C₃₁×#95	C₂³	1	2	yes	—
222	C₃₁×#95	C₂³	1	2	yes	—
223	C₃₁×#95	C₂³	1	1	yes	characteristic
224	C₃₁×#95	C₂³	1	2	yes	—
225	C₃₁×#95	C₂³	1	2	yes	—
226	C₃₁×#95	C₂³	1	2	yes	—
227	C₃₁×#95	C₂³	1	2	yes	—
228	C₃₁×#95	C₂³	1	2	yes	—
229	C₃₁×#95	C₂³	1	2	yes	—
230	C₃₁×#95	C₂³	1	1	yes	characteristic
231	C₃₁×#95	C₂³	1	1	yes	characteristic
232	C₃₁×#95	C₂³	1	1	yes	characteristic
233	C₃₁×#95	C₂³	1	1	yes	characteristic
234	C₃₁×#95	C₂³	1	2	yes	—
235	C₃₁×#95	C₂³	1	2	yes	—
236	C₃₁×#95	C₂³	1	2	yes	—
237	C₃₁×#95	C₂³	1	2	yes	—
238	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
239	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
240	C₂×Q₈×C₃₁	—	2	2	no	—
241	C₂×Q₈×C₃₁	—	2	2	no	—
242	C₂×Q₈×C₃₁	—	2	4	no	—
243	C₂×Q₈×C₃₁	—	2	4	no	—
244	C₂×Q₈×C₃₁	—	4	2	no	—
245	C₂×Q₈×C₃₁	#41	1	4	yes	—
246	C₂×D₄×C₃₁	—	2	4	no	—
247	C₂×D₄×C₃₁	—	2	2	no	—
248	C₂×D₄×C₃₁	—	2	4	no	—
249	C₂×D₄×C₃₁	—	2	2	no	—
250	C₂×D₄×C₃₁	—	2	2	no	—
251	C₂×D₄×C₃₁	—	4	2	no	—
252	C₂²×C₄×C₃₁	—	2	2	no	—
253	C₂²×C₄×C₃₁	—	2	2	no	—
254	C₂²×C₄×C₃₁	—	2	2	no	—
255	C₂²×C₄×C₃₁	—	2	2	no	—
256	C₂²×C₄×C₃₁	—	2	2	no	—
257	C₂²×C₄×C₃₁	—	2	4	no	—
258	C₂²×C₄×C₃₁	—	2	2	no	—
259	C₂²×C₄×C₃₁	—	2	2	no	—
260	C₂²×C₄×C₃₁	—	2	4	no	—
261	C₂²×C₄×C₃₁	—	2	2	no	—
262	C₂²×C₄×C₃₁	—	2	2	no	—
263	C₂²×C₄×C₃₁	—	2	4	no	—
264	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
266	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
267	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
268	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
270	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
271	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
272	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
273	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
274	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
275	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
276	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
280	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
281	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
282	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
284	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
285	C₄⋊C₄×C₃₁	—	2	2	no	—
286	C₄⋊C₄×C₃₁	—	2	2	no	—
287	C₄⋊C₄×C₃₁	—	2	2	no	—
288	C₄⋊C₄×C₃₁	—	2	2	no	—
289	C₄⋊C₄×C₃₁	—	2	4	no	—
290	C₄⋊C₄×C₃₁	—	2	4	no	—
291	C₄⋊C₄×C₃₁	—	2	4	no	—
292	C₄⋊C₄×C₃₁	—	2	2	no	—
293	C₄⋊C₄×C₃₁	—	2	2	no	—
294	C₄⋊C₄×C₃₁	—	2	2	no	—
295	C₄⋊C₄×C₃₁	—	2	4	no	—
296	C₄⋊C₄×C₃₁	—	2	4	no	—
297	C₄⋊C₄×C₃₁	—	2	4	no	—
298	C₄⋊C₄×C₃₁	—	2	4	no	—
299	C₄⋊C₄×C₃₁	—	2	2	no	—
300	C₄⋊C₄×C₃₁	—	4	2	no	—
301	C₄⋊C₄×C₃₁	—	4	2	no	—
302	C₄⋊C₄×C₃₁	—	4	2	no	—
303	C₄⋊C₄×C₃₁	—	4	2	no	—
304	C₄⋊C₄×C₃₁	—	4	2	no	—
305	C₄⋊C₄×C₃₁	—	4	2	no	—
306	C₄⋊C₄×C₃₁	#41	1	4	yes	—
307	C₄⋊C₄×C₃₁	#41	1	4	yes	—
308	C₂²⋊C₄×C₃₁	—	2	2	no	—
309	C₂²⋊C₄×C₃₁	—	2	4	no	—
310	C₂²⋊C₄×C₃₁	—	2	2	no	—
311	C₂²⋊C₄×C₃₁	—	2	2	no	—
312	C₂²⋊C₄×C₃₁	—	2	4	no	—
313	C₂²⋊C₄×C₃₁	—	2	4	no	—
314	C₂²⋊C₄×C₃₁	—	2	4	no	—
315	C₂²⋊C₄×C₃₁	—	2	4	no	—
316	C₂²⋊C₄×C₃₁	—	2	4	no	—
317	C₂²⋊C₄×C₃₁	—	2	4	no	—
318	C₂²⋊C₄×C₃₁	—	2	4	no	—
319	C₂²⋊C₄×C₃₁	—	2	4	no	—
320	C₂²⋊C₄×C₃₁	—	2	4	no	—
321	C₂²⋊C₄×C₃₁	—	2	4	no	—
322	C₂²⋊C₄×C₃₁	—	4	2	no	—
323	C₂²⋊C₄×C₃₁	—	4	2	no	—
324	C₂²⋊C₄×C₃₁	—	4	2	no	—
325	C₂²⋊C₄×C₃₁	—	4	2	no	—
326	C₂²⋊C₄×C₃₁	#41	1	4	yes	—
327	C₄²×C₃₁	—	2	2	no	—
328	C₄²×C₃₁	—	2	2	no	—
329	C₄²×C₃₁	—	2	2	no	—
330	C₄²×C₃₁	—	2	2	no	—
331	C₄²×C₃₁	—	2	2	no	—
332	C₄²×C₃₁	—	2	2	no	—
333	C₄²×C₃₁	—	2	2	no	—
334	C₄²×C₃₁	—	2	4	no	—
335	C₄²×C₃₁	—	2	4	no	—
336	C₄²×C₃₁	—	2	2	no	—
337	C₄²×C₃₁	—	2	2	no	—
338	C₄²×C₃₁	—	2	4	no	—
339	C₄²×C₃₁	—	2	4	no	—
340	C₄²×C₃₁	—	2	2	no	—
341	C₄²×C₃₁	—	2	4	no	—
342	C₄²×C₃₁	—	2	2	no	—
343	C₄²×C₃₁	—	2	2	no	—
344	C₄²×C₃₁	—	2	4	no	—
345	C₄²×C₃₁	—	2	4	no	—
346	C₄²×C₃₁	—	2	2	no	—
347	C₄²×C₃₁	—	2	2	no	—
348	C₄²×C₃₁	—	2	2	no	—
349	C₄²×C₃₁	#41	1	4	yes	—
350	#34974	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
351	C₂³×C₃₁	—	2	1	no	—
352	C₂³×C₃₁	—	2	1	no	—
353	C₂³×C₃₁	—	2	1	no	—
354	C₂³×C₃₁	—	2	1	no	—
355	C₂³×C₃₁	—	2	1	no	—
356	C₂³×C₃₁	—	2	1	no	—
357	C₂³×C₃₁	—	2	2	no	—
358	C₂³×C₃₁	—	2	2	no	—
359	C₂³×C₃₁	—	2	2	no	—
360	C₂³×C₃₁	—	2	2	no	—
361	C₂³×C₃₁	—	2	2	no	—
362	C₂³×C₃₁	—	2	2	no	—
363	C₂³×C₃₁	—	2	2	no	—
364	C₂³×C₃₁	C₂×#41	1	2	yes	—
365	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
366	Q₈×C₃₁	—	2	8	no	—
367	Q₈×C₃₁	—	4	8	no	—
368	D₄×C₃₁	—	4	8	no	—
369	D₄×C₃₁	—	4	4	no	—
370	C₂×C₄×C₃₁	—	2	8	no	—
371	C₂×C₄×C₃₁	—	2	1	no	—
372	C₂×C₄×C₃₁	—	2	1	no	—
373	C₂×C₄×C₃₁	—	2	1	no	—
374	C₂×C₄×C₃₁	—	2	1	no	—
375	C₂×C₄×C₃₁	—	2	1	no	—
376	C₂×C₄×C₃₁	—	2	1	no	—
377	C₂×C₄×C₃₁	—	2	2	no	—
378	C₂×C₄×C₃₁	—	2	2	no	—
379	C₂×C₄×C₃₁	—	2	2	no	—
380	C₂×C₄×C₃₁	—	2	1	no	—
381	C₂×C₄×C₃₁	—	2	1	no	—
382	C₂×C₄×C₃₁	—	2	2	no	—
383	C₂×C₄×C₃₁	—	2	1	no	—
384	C₂×C₄×C₃₁	—	2	1	no	—
385	C₂×C₄×C₃₁	—	2	1	no	—
386	C₂×C₄×C₃₁	—	2	1	no	—
387	C₂×C₄×C₃₁	—	2	1	no	—
388	C₂×C₄×C₃₁	—	2	1	no	—
389	C₂×C₄×C₃₁	—	2	2	no	—
390	C₂×C₄×C₃₁	—	2	1	no	—
391	C₂×C₄×C₃₁	—	2	1	no	—
392	C₂×C₄×C₃₁	—	2	2	no	—
393	C₂×C₄×C₃₁	—	2	1	no	—
394	C₂×C₄×C₃₁	—	2	1	no	—
395	C₂×C₄×C₃₁	—	2	1	no	—
396	C₂×C₄×C₃₁	—	2	1	no	—
397	C₂×C₄×C₃₁	—	2	2	no	—
398	C₂×C₄×C₃₁	—	2	2	no	—
399	C₂×C₄×C₃₁	—	2	1	no	—
400	C₂×C₄×C₃₁	—	2	2	no	—
401	C₂×C₄×C₃₁	—	2	1	no	—
402	C₂×C₄×C₃₁	—	2	1	no	—
403	C₂×C₄×C₃₁	—	2	2	no	—
404	C₂×C₄×C₃₁	—	2	2	no	—
405	C₂×C₄×C₃₁	—	2	2	no	—
406	C₂×C₄×C₃₁	—	2	2	no	—
407	C₂×C₄×C₃₁	—	2	1	no	—
408	C₂×C₄×C₃₁	—	2	2	no	—
409	C₂×C₄×C₃₁	—	2	1	no	—
410	C₂×C₄×C₃₁	—	2	1	no	—
411	C₂×C₄×C₃₁	—	2	2	no	—
412	C₂×C₄×C₃₁	—	2	2	no	—
413	C₂×C₄×C₃₁	—	2	2	no	—
414	C₂×C₄×C₃₁	—	2	1	no	—
415	C₂×C₄×C₃₁	—	2	1	no	—
416	C₂×C₄×C₃₁	—	2	2	no	—
417	C₂×C₄×C₃₁	—	2	1	no	—
418	C₂×C₄×C₃₁	—	2	1	no	—
419	C₂×C₄×C₃₁	—	2	2	no	—
420	C₂×C₄×C₃₁	—	4	4	no	—
421	C₂×C₄×C₃₁	—	4	4	no	—
422	C₂×C₄×C₃₁	—	4	8	no	—
423	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
424	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
425	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
426	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
427	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
428	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
429	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
430	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
431	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
432	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
433	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
434	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
435	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
436	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
437	#2532	C₂×C₃₁	1	2	yes	complemented
438	#2529	C₂×C₃₁	1	2	yes	complemented
439	#2512	C₂×C₃₁	1	1	yes	characteristic, complemented
440	#2508	C₂×C₃₁	1	1	yes	characteristic, complemented
441	#2495	C₂×C₃₁	1	1	yes	characteristic, complemented
442	#2491	C₂×C₃₁	1	1	yes	characteristic
443	#2479	C₂×C₃₁	1	2	yes	complemented
444	#2474	C₂×C₃₁	1	2	yes	complemented
445	#2451	C₂×C₃₁	1	1	yes	characteristic, complemented
446	#2448	C₂×C₃₁	1	1	yes	characteristic, complemented
447	#2426	C₂×C₃₁	1	1	yes	characteristic
448	#2423	C₂×C₃₁	1	1	yes	characteristic, complemented
449	#2396	C₂×C₃₁	1	2	yes	complemented
450	#2395	C₂×C₃₁	1	2	yes	complemented
451	C₄×C₄⋊Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
452	C₄×#126	C₂×C₃₁	1	2	yes	complemented
453	C₄×#124	C₂×C₃₁	1	1	yes	characteristic, complemented
454	C₄×#124	C₂×C₃₁	1	2	yes	complemented
455	C₄×C₂²⋊Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
456	C₄×#121	C₂×C₃₁	1	1	yes	characteristic
457	#2293	C₂×C₃₁	1	1	yes	characteristic, complemented
458	C₄²×Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
459	C₄×#117	C₂×C₃₁	1	1	yes	characteristic, complemented
460	C₂²×C₃₁	—	2	2	no	—
461	C₂²×C₃₁	—	2	2	no	—
462	C₂²×C₃₁	—	2	2	no	—
463	C₂²×C₃₁	—	4	1	no	—
464	C₂²×C₃₁	—	4	1	no	—
465	C₂²×C₃₁	—	4	1	no	—
466	C₂²×C₃₁	—	4	1	no	—
467	C₂²×C₃₁	—	4	2	no	—
468	C₂²×C₃₁	—	4	2	no	—
469	C₂²×C₃₁	—	4	2	no	—
470	C₂²×C₃₁	—	4	2	no	—
471	C₂²×C₃₁	—	4	2	no	—
472	C₂²×C₃₁	—	4	2	no	—
473	C₂²×C₃₁	—	4	2	no	—
474	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
475	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
476	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
477	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
478	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
479	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
480	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
481	C₄×C₃₁	—	2	4	no	—
482	C₄×C₃₁	—	2	2	no	—
483	C₄×C₃₁	—	2	2	no	—
484	C₄×C₃₁	—	2	4	no	—
485	C₄×C₃₁	—	2	2	no	—
486	C₄×C₃₁	—	2	2	no	—
487	C₄×C₃₁	—	2	2	no	—
488	C₄×C₃₁	—	2	2	no	—
489	C₄×C₃₁	—	4	1	no	—
490	C₄×C₃₁	—	4	2	no	—
491	C₄×C₃₁	—	4	1	no	—
492	C₄×C₃₁	—	4	2	no	—
493	C₄×C₃₁	—	4	1	no	—
494	C₄×C₃₁	—	4	2	no	—
495	C₄×C₃₁	—	4	1	no	—
496	C₄×C₃₁	—	4	1	no	—
497	C₄×C₃₁	—	4	1	no	—
498	C₄×C₃₁	—	4	2	no	—
499	C₄×C₃₁	—	4	2	no	—
500	C₄×C₃₁	#529	1	4	yes	—
501	C₄×C₃₁	#542	1	4	yes	—
502	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
503	C₂×#126	C₂²×C₃₁	1	2	yes	—
504	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
505	C₂×#124	C₂²×C₃₁	1	2	yes	—
506	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
507	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
508	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
509	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
510	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
511	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
512	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
513	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
514	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
515	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
516	C₂×#117	C₂²×C₃₁	1	2	yes	—
517	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
518	#400	C₂²×C₃₁	1	2	yes	—
519	#400	C₂²×C₃₁	1	2	yes	—
520	#399	C₂²×C₃₁	1	2	yes	—
521	#399	C₂²×C₃₁	1	2	yes	—
522	#398	C₂²×C₃₁	1	2	yes	—
523	#398	C₂²×C₃₁	1	2	yes	—
524	#398	C₂²×C₃₁	1	2	yes	—
525	#397	C₂²×C₃₁	1	2	yes	—
526	#397	C₂²×C₃₁	1	2	yes	—
527	#397	C₂²×C₃₁	1	2	yes	—
528	#396	C₂²×C₃₁	1	2	yes	—
529	#396	C₂²×C₃₁	1	2	yes	—
530	#395	C₂²×C₃₁	1	2	yes	—
531	#394	C₂²×C₃₁	1	2	yes	—
532	#394	C₂²×C₃₁	1	2	yes	—
533	#393	C₂²×C₃₁	1	2	yes	—
534	#391	C₂²×C₃₁	1	2	yes	—
535	#391	C₂²×C₃₁	1	1	yes	characteristic
536	#391	C₂²×C₃₁	1	1	yes	characteristic
537	#391	C₂²×C₃₁	1	2	yes	—
538	#390	C₂²×C₃₁	1	2	yes	—
539	#390	C₂²×C₃₁	1	1	yes	characteristic
540	#390	C₂²×C₃₁	1	1	yes	characteristic
541	#390	C₂²×C₃₁	1	1	yes	characteristic
542	#390	C₂²×C₃₁	1	1	yes	characteristic
543	#389	C₂²×C₃₁	1	1	yes	characteristic
544	#389	C₂²×C₃₁	1	1	yes	characteristic
545	#389	C₂²×C₃₁	1	2	yes	—
546	#389	C₂²×C₃₁	1	1	yes	characteristic
547	#389	C₂²×C₃₁	1	1	yes	characteristic
548	#389	C₂²×C₃₁	1	1	yes	characteristic
549	#389	C₂²×C₃₁	1	1	yes	characteristic
550	#388	C₂²×C₃₁	1	2	yes	—
551	#388	C₂²×C₃₁	1	2	yes	—
552	#388	C₂²×C₃₁	1	2	yes	—
553	#388	C₂²×C₃₁	1	2	yes	—
554	#388	C₂²×C₃₁	1	2	yes	—
555	#388	C₂²×C₃₁	1	2	yes	—
556	#388	C₂²×C₃₁	1	2	yes	—
557	#388	C₂²×C₃₁	1	2	yes	—
558	#388	C₂²×C₃₁	1	2	yes	—
559	#388	C₂²×C₃₁	1	2	yes	—
560	#388	C₂²×C₃₁	1	2	yes	—
561	#388	C₂²×C₃₁	1	2	yes	—
562	#387	C₂²×C₃₁	1	2	yes	—
563	#387	C₂²×C₃₁	1	2	yes	—
564	#387	C₂²×C₃₁	1	2	yes	—
565	#387	C₂²×C₃₁	1	2	yes	—
566	#386	C₂²×C₃₁	1	2	yes	—
567	#385	C₂²×C₃₁	1	2	yes	—
568	#384	C₂²×C₃₁	1	1	yes	characteristic
569	#383	C₂²×C₃₁	1	2	yes	—
570	#382	C₂²×C₃₁	1	1	yes	characteristic
571	#382	C₂²×C₃₁	1	2	yes	—
572	#380	C₂²×C₃₁	1	1	yes	characteristic
573	#380	C₂²×C₃₁	1	1	yes	characteristic
574	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
575	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
576	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
577	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
578	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
579	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
580	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
581	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
582	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
583	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
584	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
585	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
586	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
587	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
588	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
589	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
590	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
591	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
592	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
593	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
594	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
595	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
596	#376	C₂²×C₃₁	1	1	yes	characteristic
597	#376	C₂²×C₃₁	1	1	yes	characteristic
598	C₄³	C₂²×C₃₁	1	2	yes	—
599	C₄³	C₂²×C₃₁	1	1	yes	characteristic
600	C₄³	C₂²×C₃₁	1	1	yes	characteristic
601	C₂×C₃₁	—	4	2	no	—
602	C₂×C₃₁	—	8	2	no	—
603	C₂×C₃₁	C₂×#529	1	1	yes	characteristic
604	C₂×C₃₁	#3444	1	1	yes	characteristic
605	C₂×C₃₁	C₂×#542	1	1	yes	characteristic
606	C₂×C₃₁	#3481	1	1	yes	characteristic
607	C₂×C₃₁	#3482	1	1	yes	characteristic
608	C₂×C₃₁	#3482	1	1	yes	characteristic
609	C₂×C₃₁	#3483	1	1	yes	characteristic
610	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
611	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
612	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
613	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
614	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
615	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
616	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
617	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
618	C₄⋊Q₈	—	2	4	no	—
619	#126	—	2	8	no	—
620	#124	—	2	4	no	—
621	#124	—	2	8	no	—
622	C₂²⋊Q₈	—	2	4	no	—
623	#121	—	2	4	no	—
624	C₄×Q₈	—	2	4	no	—
625	C₄×Q₈	—	2	4	no	—
626	C₄×Q₈	—	2	4	no	—
627	C₄×Q₈	—	4	4	no	—
628	C₄×D₄	—	2	4	no	—
629	C₄×D₄	—	4	4	no	—
630	#117	—	2	4	no	—
631	#117	—	2	4	no	—
632	#117	—	4	4	no	—
633	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
634	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
635	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
636	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
637	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
638	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
639	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
640	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
641	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
642	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
643	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
644	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
645	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
646	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
647	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
648	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
649	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
650	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
651	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
652	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
653	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
654	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
655	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
656	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
657	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
658	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
659	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
660	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
661	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
662	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
663	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
664	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
665	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
666	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
667	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
668	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
669	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
670	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
671	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
672	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
673	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
674	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
675	C₂×C₄²	—	2	4	no	—
676	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
677	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
678	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
679	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
680	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
681	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
682	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
683	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
684	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
685	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
686	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
687	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
688	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
689	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
690	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
691	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
692	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
693	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
694	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
695	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
696	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
697	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
698	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
699	#95	C₂³×C₃₁	1	1	yes	characteristic
700	#95	C₂³×C₃₁	1	1	yes	characteristic
701	#95	C₂³×C₃₁	1	1	yes	characteristic
702	#95	C₂³×C₃₁	1	1	yes	characteristic
703	#95	C₂³×C₃₁	1	1	yes	characteristic
704	#95	C₂³×C₃₁	1	1	yes	characteristic
705	#95	C₂³×C₃₁	1	1	yes	characteristic
706	#95	C₂³×C₃₁	1	1	yes	characteristic
707	#95	C₂³×C₃₁	1	2	yes	—
708	#95	C₂³×C₃₁	1	2	yes	—
709	#95	C₂³×C₃₁	1	2	yes	—
710	#95	C₂³×C₃₁	1	2	yes	—
711	#95	C₂³×C₃₁	1	2	yes	—
712	#95	C₂³×C₃₁	1	2	yes	—
713	#95	C₂³×C₃₁	1	2	yes	—
714	#95	C₂³×C₃₁	1	2	yes	—
715	#95	C₂³×C₃₁	1	2	yes	—
716	#95	C₂³×C₃₁	1	2	yes	—
717	#95	C₂³×C₃₁	1	2	yes	—
718	#95	C₂³×C₃₁	1	2	yes	—
719	#95	C₂³×C₃₁	1	2	yes	—
720	#95	C₂³×C₃₁	1	2	yes	—
721	#95	C₂³×C₃₁	1	2	yes	—
722	#95	C₂³×C₃₁	1	2	yes	—
723	#95	C₂³×C₃₁	1	2	yes	—
724	#95	C₂³×C₃₁	1	2	yes	—
725	C₃₁	#34974	1	1	yes	characteristic, direct product factor, Sylow
726	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
727	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
728	C₂×Q₈	—	2	2	no	—
729	C₂×Q₈	—	2	2	no	—
730	C₂×Q₈	—	2	4	no	—
731	C₂×Q₈	—	2	4	no	—
732	C₂×Q₈	—	4	2	no	—
733	C₂×Q₈	#41×C₃₁	1	4	yes	—
734	C₂×D₄	—	2	4	no	—
735	C₂×D₄	—	2	2	no	—
736	C₂×D₄	—	2	4	no	—
737	C₂×D₄	—	2	2	no	—
738	C₂×D₄	—	2	2	no	—
739	C₂×D₄	—	4	2	no	—
740	C₂²×C₄	—	2	2	no	—
741	C₂²×C₄	—	2	2	no	—
742	C₂²×C₄	—	2	2	no	—
743	C₂²×C₄	—	2	2	no	—
744	C₂²×C₄	—	2	2	no	—
745	C₂²×C₄	—	2	4	no	—
746	C₂²×C₄	—	2	2	no	—
747	C₂²×C₄	—	2	2	no	—
748	C₂²×C₄	—	2	4	no	—
749	C₂²×C₄	—	2	2	no	—
750	C₂²×C₄	—	2	2	no	—
751	C₂²×C₄	—	2	4	no	—
752	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
753	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
754	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
755	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
756	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
757	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
758	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
759	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
760	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
761	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
762	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
763	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
764	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
765	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
766	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
767	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
768	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
769	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
770	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
771	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
772	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
773	C₄⋊C₄	—	2	2	no	—
774	C₄⋊C₄	—	2	2	no	—
775	C₄⋊C₄	—	2	2	no	—
776	C₄⋊C₄	—	2	2	no	—
777	C₄⋊C₄	—	2	4	no	—
778	C₄⋊C₄	—	2	4	no	—
779	C₄⋊C₄	—	2	4	no	—
780	C₄⋊C₄	—	2	2	no	—
781	C₄⋊C₄	—	2	2	no	—
782	C₄⋊C₄	—	2	2	no	—
783	C₄⋊C₄	—	2	4	no	—
784	C₄⋊C₄	—	2	4	no	—
785	C₄⋊C₄	—	2	4	no	—
786	C₄⋊C₄	—	2	4	no	—
787	C₄⋊C₄	—	2	2	no	—
788	C₄⋊C₄	—	4	2	no	—
789	C₄⋊C₄	—	4	2	no	—
790	C₄⋊C₄	—	4	2	no	—
791	C₄⋊C₄	—	4	2	no	—
792	C₄⋊C₄	—	4	2	no	—
793	C₄⋊C₄	—	4	2	no	—
794	C₄⋊C₄	#41×C₃₁	1	4	yes	—
795	C₄⋊C₄	#41×C₃₁	1	4	yes	—
796	C₂²⋊C₄	—	2	2	no	—
797	C₂²⋊C₄	—	2	4	no	—
798	C₂²⋊C₄	—	2	2	no	—
799	C₂²⋊C₄	—	2	2	no	—
800	C₂²⋊C₄	—	2	4	no	—
801	C₂²⋊C₄	—	2	4	no	—
802	C₂²⋊C₄	—	2	4	no	—
803	C₂²⋊C₄	—	2	4	no	—
804	C₂²⋊C₄	—	2	4	no	—
805	C₂²⋊C₄	—	2	4	no	—
806	C₂²⋊C₄	—	2	4	no	—
807	C₂²⋊C₄	—	2	4	no	—
808	C₂²⋊C₄	—	2	4	no	—
809	C₂²⋊C₄	—	2	4	no	—
810	C₂²⋊C₄	—	4	2	no	—
811	C₂²⋊C₄	—	4	2	no	—
812	C₂²⋊C₄	—	4	2	no	—
813	C₂²⋊C₄	—	4	2	no	—
814	C₂²⋊C₄	#41×C₃₁	1	4	yes	—
815	C₄²	—	2	2	no	—
816	C₄²	—	2	2	no	—
817	C₄²	—	2	2	no	—
818	C₄²	—	2	2	no	—
819	C₄²	—	2	2	no	—
820	C₄²	—	2	2	no	—
821	C₄²	—	2	2	no	—
822	C₄²	—	2	4	no	—
823	C₄²	—	2	4	no	—
824	C₄²	—	2	2	no	—
825	C₄²	—	2	2	no	—
826	C₄²	—	2	4	no	—
827	C₄²	—	2	4	no	—
828	C₄²	—	2	2	no	—
829	C₄²	—	2	4	no	—
830	C₄²	—	2	2	no	—
831	C₄²	—	2	2	no	—
832	C₄²	—	2	4	no	—
833	C₄²	—	2	4	no	—
834	C₄²	—	2	2	no	—
835	C₄²	—	2	2	no	—
836	C₄²	—	2	2	no	—
837	C₄²	#41×C₃₁	1	4	yes	—
838	C₂³	—	2	1	no	—
839	C₂³	—	2	1	no	—
840	C₂³	—	2	1	no	—
841	C₂³	—	2	1	no	—
842	C₂³	—	2	1	no	—
843	C₂³	—	2	1	no	—
844	C₂³	—	2	2	no	—
845	C₂³	—	2	2	no	—
846	C₂³	—	2	2	no	—
847	C₂³	—	2	2	no	—
848	C₂³	—	2	2	no	—
849	C₂³	—	2	2	no	—
850	C₂³	—	2	2	no	—
851	C₂³	C₂×#41×C₃₁	1	2	yes	—
852	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
853	Q₈	—	2	8	no	—
854	Q₈	—	4	8	no	—
855	D₄	—	4	8	no	—
856	D₄	—	4	4	no	—
857	C₂×C₄	—	2	8	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	2	2	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	2	2	no	—
867	C₂×C₄	—	2	1	no	—
868	C₂×C₄	—	2	1	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	1	no	—
874	C₂×C₄	—	2	1	no	—
875	C₂×C₄	—	2	1	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	1	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	1	no	—
881	C₂×C₄	—	2	1	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	2	1	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	1	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	1	no	—
897	C₂×C₄	—	2	1	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	1	no	—
902	C₂×C₄	—	2	1	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	1	no	—
905	C₂×C₄	—	2	1	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	4	4	no	—
908	C₂×C₄	—	4	4	no	—
909	C₂×C₄	—	4	8	no	—
910	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
911	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
912	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
913	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
914	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
915	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
916	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
917	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
918	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
919	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
920	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
921	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
922	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
923	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
924	C₂²	—	2	2	no	—
925	C₂²	—	2	2	no	—
926	C₂²	—	2	2	no	—
927	C₂²	—	4	1	no	—
928	C₂²	—	4	1	no	—
929	C₂²	—	4	1	no	—
930	C₂²	—	4	1	no	—
931	C₂²	—	4	2	no	—
932	C₂²	—	4	2	no	—
933	C₂²	—	4	2	no	—
934	C₂²	—	4	2	no	—
935	C₂²	—	4	2	no	—
936	C₂²	—	4	2	no	—
937	C₂²	—	4	2	no	—
938	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
939	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
940	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
941	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
942	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
943	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
944	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
945	C₄	—	2	4	no	—
946	C₄	—	2	2	no	—
947	C₄	—	2	2	no	—
948	C₄	—	2	4	no	—
949	C₄	—	2	2	no	—
950	C₄	—	2	2	no	—
951	C₄	—	2	2	no	—
952	C₄	—	2	2	no	—
953	C₄	—	4	1	no	—
954	C₄	—	4	2	no	—
955	C₄	—	4	1	no	—
956	C₄	—	4	2	no	—
957	C₄	—	4	2	no	—
958	C₄	—	4	1	no	—
959	C₄	—	4	1	no	—
960	C₄	—	4	1	no	—
961	C₄	—	4	1	no	—
962	C₄	—	4	2	no	—
963	C₄	—	4	2	no	—
964	C₄	C₃₁×#529	1	4	yes	—
965	C₄	C₃₁×#542	1	4	yes	—
966	C₂	—	4	2	no	—
967	C₂	—	8	2	no	—
968	C₂	C₂×C₃₁×#529	1	1	yes	characteristic
969	C₂	C₃₁×#3444	1	1	yes	characteristic
970	C₂	C₂×C₃₁×#542	1	1	yes	characteristic
971	C₂	C₃₁×#3481	1	1	yes	characteristic
972	C₂	C₃₁×#3482	1	1	yes	characteristic
973	C₂	C₃₁×#3482	1	1	yes	characteristic
974	C₂	C₃₁×#3483	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₃₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃₁
socle	C₂³×C₃₁	C₂⁵
prime radical	C₂×C₃₁×#121	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₃₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₃₁×#2532	C₂	semidirect
2. C₃₁×#2529	C₂	semidirect
3. C₃₁×#2512	C₂	semidirect
4. C₃₁×#2508	C₂	semidirect
5. C₃₁×#2495	C₂	semidirect
7. C₃₁×#2479	C₂	semidirect
8. C₃₁×#2474	C₂	semidirect
9. C₃₁×#2451	C₂	semidirect
10. C₃₁×#2448	C₂	semidirect
12. C₃₁×#2423	C₂	semidirect
13. C₃₁×#2396	C₂	semidirect
14. C₃₁×#2395	C₂	semidirect
15. C₄×C₃₁×C₄⋊Q₈	C₂	semidirect
16. C₄×C₃₁×#126	C₂	semidirect
17. C₄×C₃₁×#124	C₂	semidirect
18. C₄×C₃₁×#124	C₂	semidirect
19. C₄×C₃₁×C₂²⋊Q₈	C₂	semidirect
21. C₃₁×#2293	C₂	semidirect
22. C₄²×Q₈×C₃₁	C₂	semidirect
23. C₄×C₃₁×#117	C₂	semidirect
350. #34974	C₃₁	direct (N × H)
437. #2532	C₂×C₃₁	semidirect
438. #2529	C₂×C₃₁	semidirect
439. #2512	C₂×C₃₁	semidirect
440. #2508	C₂×C₃₁	semidirect
441. #2495	C₂×C₃₁	semidirect
443. #2479	C₂×C₃₁	semidirect
444. #2474	C₂×C₃₁	semidirect
445. #2451	C₂×C₃₁	semidirect
446. #2448	C₂×C₃₁	semidirect
448. #2423	C₂×C₃₁	semidirect
449. #2396	C₂×C₃₁	semidirect
450. #2395	C₂×C₃₁	semidirect
451. C₄×C₄⋊Q₈	C₂×C₃₁	semidirect
452. C₄×#126	C₂×C₃₁	semidirect
453. C₄×#124	C₂×C₃₁	semidirect
454. C₄×#124	C₂×C₃₁	semidirect
455. C₄×C₂²⋊Q₈	C₂×C₃₁	semidirect
457. #2293	C₂×C₃₁	semidirect
458. C₄²×Q₈	C₂×C₃₁	semidirect
459. C₄×#117	C₂×C₃₁	semidirect
725. C₃₁	#34974	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃₁×#2532	2
C₃₁×#2529	2
C₃₁×#2512	2
C₃₁×#2508	2
C₃₁×#2495	2
C₃₁×#2491	2
C₃₁×#2479	2
C₃₁×#2474	2
C₃₁×#2451	2
C₃₁×#2448	2
C₃₁×#2426	2
C₃₁×#2423	2
C₃₁×#2396	2
C₃₁×#2395	2
C₄×C₃₁×C₄⋊Q₈	2
C₄×C₃₁×#126	2
C₄×C₃₁×#124	2
C₄×C₃₁×C₂²⋊Q₈	2
C₄×C₃₁×#121	2
C₃₁×#2293	2
C₄²×Q₈×C₃₁	2
C₄×C₃₁×#117	2
#34974	31

Subgroups — C31×#34974 #21491733

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#34974 #21491733